19、保密约束下的信源编码与无线信道密钥提取

保密约束下的信源编码与无线信道密钥提取

1. 保密约束下的信源编码

在保密约束下的信源编码中，对于密钥率有如下推导：
$$NR_k \geq \log M_k \geq H(W_k)$$
$$\geq H(W_k|J, M_B) - H(W_k|J, \hat{A} N, M_B)$$
$$= H(\hat{A}_N|J, M_B) - H(\hat{A}_N|J, W_k, M_B)$$
$$= H(\hat{A}_N|J, M_B) \quad (8.54)$$
$$\geq N(\epsilon - \epsilon) - H(A_N|J) + H(\hat{A}_N|J, M_B) \quad (8.55)$$
$$\geq N(\epsilon - \epsilon) - NH(A) + I(A_N; J) - I(\hat{A}_N; J, M_B) + I(A_N; \hat{A}_N)$$
$$ + H(\hat{A}_N|A_N) \quad (8.56)$$
$$\geq N(\epsilon - H(A) - \epsilon) + \sum {m = 1}^{N} I(A_m; \hat{A} m) + I(A_N; J, M_B) - I(\hat{A}_N; J, M_B)$$
$$ + H(\hat{A}_N|A_N) \quad (8.57)$$
$$= N(\epsilon - H(A) - \epsilon) + \sum {m = 1}^{N} I(A_m; \hat{A} m) + H(A_N|A_N, J, M_B)$$